Existence and uniqueness results for a non linear stochastic partial differential equation

1987 ◽  
pp. 1-24 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Existence And Uniqueness ◽  
Stochastic Partial Differential Equation ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Non Linear

scholarly journals About a Partial Differential Equation-Based Interpolator for Signal Envelope Computing: Existence Results and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Oumar Niang ◽  
Abdoulaye Thioune ◽  
Éric Deléchelle ◽  
Mary Teuw Niane ◽  
Jacques Lemoine
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mathematical Problem ◽  
Existence Results ◽  
Test Results ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mode Decomposition ◽  
Characteristic Points

This paper models and solves the mathematical problem of interpolating characteristic points of signals by a partial differential Equation-(PDE-) based approach. The existence and uniqueness results are established in an appropriate space whose regularity is similar to cubic spline one. We show how this space is suitable for the empirical mode decomposition (EMD) sifting process. Numerical schemes and computing applications are also presented for signal envelopes calculation. The test results show the usefulness of the new PDE interpolator in some pathological cases like input class functions that are not so regular as in the cubic splines case. Some image filtering tests strengthen the demonstration of PDE interpolator performance.

MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (02) ◽  
pp. 271-294 ◽  
Author(s):  
B. BOUFOUSSI ◽  
N. MRHARDY
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Partial Differential Equation ◽  
Yosida Approximation ◽  
Partial Differential ◽  
Doubly Stochastic ◽  
Uniqueness Of The Solution

In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.

scholarly journals Smoothing the domain out for positive solutions

2000 ◽  
Vol 61 (3) ◽  
pp. 405-413 ◽  
Author(s):  
Yaping Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Partial Differential Equation ◽  
Irregular Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Analytical Tools ◽  
The Given

For a given nonlinear partial differential equation defined on a bounded domain with irregular boundary, the available analytical tools are very limited in relation to the study of positive solutions. In this paper wer first use weak convergence methods to show that for an elliptic equation of a certain type, classical positive solutions on nearby smooth domains approach a generalised positive solution on the given domain. The idea is then applied to sublinear elliptic problems to obtain existence and uniqueness results.

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